Force particles outwards and upward
Turn off gravity  for both methods.
Using a curve force
Use multiple emitters on multiple layers. Add a curve force to each layer shaping the path of the particles as desired.
Using physical forces
Force this setup I used Wind forces (for the up and down movement), a point force (to disperse the particles at the bottom and a vortex force on the bottom to stop them from drifting away on the horizontal plane.

The wind forces
Use a smaller wind force to push the particles downward (strength -20) with a narrow falloff (0.8, 1.2).
Use a larger wind force to push the particles upward (strength 10). It will also act in the center (where the particles are supposed to go down), which is why the smaller down force has a larger strength to counteract the upward force.
Outward movement at the bottom
A simple point force at the bottom with a radius of 1 - 2 can push the particles away from the center. Since the continue to drift away from the center, a vortex force can pull them back towards it. Here you need to fine tune the value to stop the particles from not following the desired path.
You can use drag forces to remove the XZ velocities. A drag force in combination with a strong wind force will give you good control and can remove some problematic velocity which has built up.